Evaluating the incompleteness of machine-generated summaries remains a critical challenge in natural language generation. In domains such as healthcare, education, and policy, summaries that omit or distort key content can appear fluent yet undermine reliability and trust. We introduce a Lie algebra–based semantic flow framework that treats summarization as a geometric transformation in embedding space, where incompleteness manifests as segments with low semantic flow magnitudes. Unlike prior metrics that collapse evaluation into a single similarity score, our approach provides interpretable, segment-level signals through a dynamic mean-scaled thresholding mechanism, requiring no supervision. We evaluate our method on UniSumEval and SIGHT benchmarks, showing significant improvements over existing methods. Qualitative analysis further demonstrates that our framework not only identifies diverse forms of incompleteness but also provides actionable, interpretable signals for human-in-the-loop review.